less than (lessThan)

(lessThan number1 number2) is true just in case the Quantity number1 is less than the Quantity number2.

Ontology

SUMO / BASE-ONTOLOGY

Class(es)

class

inheritable relation

binary predicate
is instance of

transitive relation
is instance of

irreflexive relation
is instance of

class

inheritable relation

relation extended to quantities
is instance of

less than

Coordinate term(s)

addition fn back fn division fn exponentiation fn front fn max fn min fn multiplication fn reciprocal fn remainder fn round fn subtraction fn arc weight attribute authors before before or equal causes causes subclass citizen closed on connected connected engineering components contains information cooccur copy crosses date decreases likelihood developmental form disjoint distributes documentation duration during earlier editor element employs equal equivalence relation on exploits expressed in language faces family relation finishes frequency graph part greater than greater than or equal to has purpose has skill holds during holds obligation holds right hole identity element in list in scope of interest increases likelihood independent probability inhabits inhibits initial list instance interior part inverse irreflexive on larger less than or equal to manner material measure meets spatially meets temporally modal attribute overlaps partially overlaps temporally parent partial ordering on partly located path length possesses precondition prevents proper part property publishes range range subclass refers reflexive on related internal concept sibling smaller starts sub attribute sub collection sub graph sub list sub organizations sub plan sub process sub proposition subclass subrelation subsumes content class subsumes content instance successor attribute successor attribute closure superficial part temporal part time total ordering on trichotomizing on uses valence version

Type restrictions

lessThan(quantity, quantity)

Related WordNet synsets

less: smaller in amount or degree: "the less I see of you the better"; "people have lost their heads for less"

See more related synsets on a separate page.

Axioms (21)

less than is trichotomizing on real number.

(trichotomizingOn lessThan RealNumber)

greater than is an inverse of less than.

(inverse greaterThan lessThan)

number1 is less than or equal to number2 if and only if number1 is equal to number2 or number1 is less than number2.

(<=>
      (lessThanOrEqualTo ?NUMBER1 ?NUMBER2)
      (or
            (equal ?NUMBER1 ?NUMBER2)
            (lessThan ?NUMBER1 ?NUMBER2)))

number is an instance of negative real number if and only if number is less than and number is an instance of real number.

(<=>
      (instance ?NUMBER NegativeRealNumber)
      (and
            (lessThan ?NUMBER 0)
            (instance ?NUMBER RealNumber)))

rel is an instance of total valued relation if and only if there exists valence so that rel is an instance of relation and rel %&has valence argument(s) and

if for all number,element,class holds: if number is less than valence and the number number argument of rel is an instance of class and element is equal to "numberth element of "()"", then element is an instance of class,
then there exists item so that rel(,item) holds

(<=>
      (instance ?REL TotalValuedRelation)
      (exists
            (?VALENCE)
            (and
                  (instance ?REL Relation)
                  (valence ?REL ?VALENCE)
                  (=>
                        (forall
                              (?NUMBER ?ELEMENT ?CLASS)
                              (=>
                                    (and
                                          (lessThan ?NUMBER ?VALENCE)
                                          (domain ?REL ?NUMBER ?CLASS)
                                          (equal
                                                ?ELEMENT
                                                (ListOrderFn
                                                      (ListFn @ROW)
                                                      ?NUMBER)))
                                    (instance ?ELEMENT ?CLASS)))
                        (exists
                              (?ITEM)
                              (holds ?REL @ROW ?ITEM))))))

If formula1 decreases likelihood of formula2 and "the probability of formula2" is equal to number1 and probability of formula1 provided that formula2 holds is formula2, then number2 is less than number1.

(=>
      (and
            (decreasesLikelihood ?FORMULA1 ?FORMULA2)
            (equal
                  (ProbabilityFn ?FORMULA2)
                  ?NUMBER1)
            (conditionalProbability ?FORMULA1 ?FORMULA2 ?NUMBER2))
      (lessThan ?NUMBER2 ?NUMBER1))

if list is an instance of list,
then there exists number1 so that there exists item1 so that "number1th element of list" is not equal to item1 and for all number2 holds: if number2 is an instance of positive integer and number2 is less than number1, then there exists item2 so that "number2th element of list" is equal to item2

(=>
      (instance ?LIST List)
      (exists
            (?NUMBER1)
            (exists
                  (?ITEM1)
                  (and
                        (not
                              (equal
                                    (ListOrderFn ?LIST ?NUMBER1)
                                    ?ITEM1))
                        (forall
                              (?NUMBER2)
                              (=>
                                    (and
                                          (instance ?NUMBER2 PositiveInteger)
                                          (lessThan ?NUMBER2 ?NUMBER1))
                                    (exists
                                          (?ITEM2)
                                          (equal
                                                (ListOrderFn ?LIST ?NUMBER2)
                                                ?ITEM2))))))))

If "the ceiling of number" is equal to int, then there doesn't exist integer otherint so that otherint is greater than or equal to number and otherint is less than int.

(=>
      (equal
            (CeilingFn ?NUMBER)
            ?INT)
      (not
            (exists
                  (?OTHERINT)
                  (and
                        (instance ?OTHERINT Integer)
                        (greaterThanOrEqualTo ?OTHERINT ?NUMBER)
                        (lessThan ?OTHERINT ?INT)))))

if "the least common multiple of " is equal to number,
then there doesn't exist less so that less is less than number and for all element holds: if element is a member of "()", then "less mod element" is equal to

(=>
      (equal
            (LeastCommonMultipleFn @ROW)
            ?NUMBER)
      (not
            (exists
                  (?LESS)
                  (and
                        (lessThan ?LESS ?NUMBER)
                        (forall
                              (?ELEMENT)
                              (=>
                                    (inList
                                          ?ELEMENT
                                          (ListFn @ROW))
                                    (equal
                                          (RemainderFn ?LESS ?ELEMENT)
                                          0)))))))

If "the smaller of number1 and number2" is equal to number, then

number is equal to number1 and number1 is less than number2
number is equal to number2 and number2 is less than number1
number is equal to number1 and number is equal to number2

(=>
      (equal
            (MinFn ?NUMBER1 ?NUMBER2)
            ?NUMBER)
      (or
            (and
                  (equal ?NUMBER ?NUMBER1)
                  (lessThan ?NUMBER1 ?NUMBER2))
            (and
                  (equal ?NUMBER ?NUMBER2)
                  (lessThan ?NUMBER2 ?NUMBER1))
            (and
                  (equal ?NUMBER ?NUMBER1)
                  (equal ?NUMBER ?NUMBER2))))

if "number1 rounded" is equal to number2,
then
- if "(number1-"the largest integer less than or equal to number1")" is less than , then number2 is equal to "the largest integer less than or equal to number1"
- if "(number1-"the largest integer less than or equal to number1")" is greater than or equal to , then number2 is equal to "the ceiling of number1"

(=>
      (equal
            (RoundFn ?NUMBER1)
            ?NUMBER2)
      (or
            (=>
                  (lessThan
                        (SubtractionFn
                              ?NUMBER1
                              (FloorFn ?NUMBER1))
                        0.5)
                  (equal
                        ?NUMBER2
                        (FloorFn ?NUMBER1)))
            (=>
                  (greaterThanOrEqualTo
                        (SubtractionFn
                              ?NUMBER1
                              (FloorFn ?NUMBER1))
                        0.5)
                  (equal
                        ?NUMBER2
                        (CeilingFn ?NUMBER1)))))

If int is an instance of integer, then int is less than "(int+1)".

(=>
      (instance ?INT Integer)
      (lessThan
            ?INT
            (SuccessorFn ?INT)))

If int1 is an instance of integer and int2 is an instance of integer, then int1 is not less than int2 or int2 is not less than "(int1+1)".

(=>
      (and
            (instance ?INT1 Integer)
            (instance ?INT2 Integer))
      (not
            (and
                  (lessThan ?INT1 ?INT2)
                  (lessThan
                        ?INT2
                        (SuccessorFn ?INT1)))))

If int1 is an instance of integer and int2 is an instance of integer, then int2 is not less than int1 or "(int1+2)" is not less than int2.

(=>
      (and
            (instance ?INT1 Integer)
            (instance ?INT2 Integer))
      (not
            (and
                  (lessThan ?INT2 ?INT1)
                  (lessThan
                        (PredecessorFn ?INT1)
                        ?INT2))))

There don't exist the set of paths that partition graph into two separate graphs path1,the set of minimal paths that partition graph into two separate graphs path2 so that the length of path1 is number1 and the length of path2 is number2 and number1 is less than number2.

(not
      (exists
            (?PATH1 ?PATH2)
            (and
                  (instance
                        ?PATH1
                        (CutSetFn ?GRAPH))
                  (instance
                        ?PATH2
                        (MinimalCutSetFn ?GRAPH))
                  (pathLength ?PATH1 ?NUMBER1)
                  (pathLength ?PATH2 ?NUMBER2)
                  (lessThan ?NUMBER1 ?NUMBER2))))

If hour is an instance of "the hour number", then number is less than .

(=>
      (instance
            ?HOUR
            (HourFn ?NUMBER ?DAY))
      (lessThan ?NUMBER 24))

If minute is an instance of "the minute number", then number is less than .

(=>
      (instance
            ?MINUTE
            (MinuteFn ?NUMBER ?HOUR))
      (lessThan ?NUMBER 60))

If second is an instance of "the second number", then number is less than .

(=>
      (instance
            ?SECOND
            (SecondFn ?NUMBER ?MINUTE))
      (lessThan ?NUMBER 60))

If decrease is an instance of decreasing and obj is a patient of decrease, then there exist unit,quant1,quant2 so that "obj unit(s)" is equal to quant1 immediately before "the time of existence of decrease" and "obj unit(s)" is equal to quant2 immediately after "the time of existence of decrease" and quant2 is less than quant1.

(=>
      (and
            (instance ?DECREASE Decreasing)
            (patient ?DECREASE ?OBJ))
      (exists
            (?UNIT ?QUANT1 ?QUANT2)
            (and
                  (holdsDuring
                        (ImmediatePastFn
                              (WhenFn ?DECREASE))
                        (equal
                              (MeasureFn ?OBJ ?UNIT)
                              ?QUANT1))
                  (holdsDuring
                        (ImmediateFutureFn
                              (WhenFn ?DECREASE))
                        (equal
                              (MeasureFn ?OBJ ?UNIT)
                              ?QUANT2))
                  (lessThan ?QUANT2 ?QUANT1))))

If cool is an instance of cooling and obj is a patient of cool, then there exist temperature measure unit,quant1,quant2 so that "obj unit(s)" is equal to quant1 immediately before "the time of existence of cool" and "obj unit(s)" is equal to quant2 immediately after "the time of existence of cool" and quant2 is less than quant1.

(=>
      (and
            (instance ?COOL Cooling)
            (patient ?COOL ?OBJ))
      (exists
            (?UNIT ?QUANT1 ?QUANT2)
            (and
                  (instance ?UNIT TemperatureMeasure)
                  (holdsDuring
                        (ImmediatePastFn
                              (WhenFn ?COOL))
                        (equal
                              (MeasureFn ?OBJ ?UNIT)
                              ?QUANT1))
                  (holdsDuring
                        (ImmediateFutureFn
                              (WhenFn ?COOL))
                        (equal
                              (MeasureFn ?OBJ ?UNIT)
                              ?QUANT2))
                  (lessThan ?QUANT2 ?QUANT1))))

if
- path1 is path along with process occurs
- process origins at source
- process ends at dest
- the length of path1 is measure1
- there don't exist path2,measure2 so that path2 is path along with process occurs and process origins at origin and process ends at dest and the length of path2 is measure2 and measure2 is less than measure1
,
then for all obj holds: if obj is a part of path1, then obj is between source and dest

(=>
      (and
            (path ?PROCESS ?PATH1)
            (origin ?PROCESS ?SOURCE)
            (destination ?PROCESS ?DEST)
            (length ?PATH1 ?MEASURE1)
            (not
                  (exists
                        (?PATH2 ?MEASURE2)
                        (and
                              (path ?PROCESS ?PATH2)
                              (origin ?PROCESS ?ORIGIN)
                              (destination ?PROCESS ?DEST)
                              (length ?PATH2 ?MEASURE2)
                              (lessThan ?MEASURE2 ?MEASURE1)))))
      (forall
            (?OBJ)
            (=>
                  (part ?OBJ ?PATH1)
                  (between ?SOURCE ?OBJ ?DEST))))